Expand Using the Binomial Theorem (x+12)^2

Problem

(x+12)2

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=x b=12 and n=2

2. Apply the formula for the Binomial Theorem, which states (a+b)n=(∑_k=0^n)((n/k))*a(n−k)*bk)

3. Write out the terms of the expansion using the combinations (2/0)) (2/1)) and (2/2))

(x+12)2=(2/0)x2*(12)0+(2/1)x1*(12)1+(2/2)x0*(12)2)))

4. Calculate the binomial coefficients and the powers of 12.

(x+12)2=1⋅x2⋅1+2⋅x⋅12+1⋅1⋅144

5. Simplify each term to find the final polynomial.

(x+12)2=x2+24*x+144

Final Answer

(x+12)2=x2+24*x+144

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